130 Chapter 2 Linear Equations and Inequalities Translating to a Linear Equation Forty less than five times a number is fifty-two less than the number. Find the number. Solution: less is less Step 1: Read the problem. Let x represent the unknown number. Step 2: Label the unknown. Step 4: Write an equation. Step 5: Solve the equation. a 5 times b 1402 a the b 1522 a number number 5x 40 x 52 5x 40 x 52 5x x 40 x x 52 4x 40 52 4x 40 40 52 40 4x 12 4x 4 12 4 The number is Step 6: Write the final answer in words. 3. Skill Practice 2. Thirteen more than twice a number is 5 more than the number. Find the number. Translating to a Linear Equation Twice the sum of a number and six is two more than three times the number. Find the number. Solution: Step 1: Read the problem. Let x represent the unknown number. Step 2: Label the unknown. twice the sum is 2 more than Step 3: Write a verbal model. Step 4: Write an equation. 2 1x 62 3x 2 three times a number Example 3 x 3 Example 2 Step 3: Write a verbal model. Avoiding Mistakes It is important to remember that subtraction is not a commutative operation. Therefore, the order in which two real numbers are subtracted affects the outcome. The expression “forty less than five times a number” must be translated 5x 40 1not 40 5x2 as: . Similarly, “fifty-two less than the number” must be translated as: x 52 1not 52 x2. Answer 2. The number is 8.
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